SÃO PAULO—Vast fires, many of them set by loggers, are ravaging the Amazon at a rate not seen in years, sending plumes of smoke that darken skies over Brazilian cities at a time when there is international pushback against President Jair Bolsonaro’s environmental policies.

Smoke from the Amazon, as well as blazes across Brazil’s western savanna, has spread over swaths of the country, with darkness descending on São Paulo by midafternoon Monday, two hours earlier than normal. Residents posted photos on social media of blackened...